Given that it works after 10 mins, it makes it much harder to understand why it doesn't work to start with. Does it always eventually work?

I'm not sure what type of speedo you have fitted (ie digital which would be driven by a sensor in the transmission) or one driven by a wheel sensor.

It would appear that you may have a loose connection and you may have to acquire a workshop manual which will give you the necessary wiring diagram to trace the circuit and find the fault